Suggestions!

http://www.mangago.me/read-manga/hachimitsu_darling/ (vet)
http://www.mangago.me/read-manga/hajishirazu_na_yoru/ ch.2 (vet)
http://www.mangago.me/read-manga/kyou_hana_no_gotoshi/ ch.5 (pet shop)
http://www.mangago.me/read-manga/kamatte_kawaii_hito/ (cat cafe)
http://www.mangago.me/read-manga/harapeko_usagi_to_koisuru_ookami/ (rabbit cafe)

http://www.mangago.me/read-manga/koukyuu_no_arika/ (dog trainer)
http://www.mangago.me/read-manga/kawaita_yoru_no_machi_wo_oyogu/tr/63417/page/133/ (dog contest)

cats:
http://www.mangago.me/read-manga/smoker/ from ch.5 (animal shelter)
http://www.mangago.me/read-manga/neko_chan/
http://www.mangago.me/read-manga/kuroneko_wa_shippo_de_amaeru/
http://www.mangago.me/read-manga/koi_to_wa_yobenai/
http://www.mangago.me/read-manga/gravity_eyes/
http://www.mangago.me/read-manga/boku_to_neko_to_hatsukoi_kousa/

Not sure it's too wide for your request or not as it contains all cute pets in manga. - I'm pet lover.
http://www.mangago.me/people/tag/2337/Cute+Pet/

Btw it's all yaoi. I didn't even notice you hadn't specified a genre, sorry about that. It's just a bad habit of mine (￣∇￣")

Me too. If no specify other genre, I automatically assume it's yaoi/shounen-ai. HA+ (▰˘◡˘▰)

Yeah, I just assume that everyone wants to read yaoi (￣∇￣") I'm glad I'm not the only one ^^

Thanks!

Dont worry, I mostly read yaoi anyways (⌒▽⌒) but I don't mind suggestions for shoujo mangas (=・ω・=) Thanks you two!

Yaoi is all that matters ε=ε=(ノ≧∇≦)ノ haha Thanks for your suggestions (⌒▽⌒)

You can also check out my list. http://www.mangago.me/home/mangalist/26459/

Thank you! :D